Dr Emilio Pierro

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Students must have completed Introduction to Abstract Mathematics (MA103) and Mathematical Methods (MA100).

The aim of this course is to continue (from MA103) the study of abstract algebraic structures. There are two main strands in the course. First, we develop further the theory of groups, using permutation groups as a key example. We investigate the important concepts of normal subgroups and quotient groups. Secondly, we introduce rings, and study factorisation in rings, where we also look at some connections with number theory. Groups: Review of basic group theory; permutations and permutation groups; homomorphisms; conjugation, normal subgroups and quotient groups; the first isomorphism theorem for groups. Rings: basic properties of rings and examples (including polynomial rings, matrix rings, and number rings); subrings, ideals and ring homomorphisms; divisibility in integral domains; greatest common divisors; Euclidean rings and unique factorisation; applications to number theory; principal ideal domains.

This course is delivered through a combination of classes and lectures, totalling a minimum of 30 hours across Michaelmas Term. This year teaching will be delivered face-to-face.

Written answers to set problems will be expected on a weekly basis.

A Book of Abstract Algebra, Charles C Pinter, (Dover, 2nd edition, 2010);

Introduction to Algebra, Peter J Cameron (OUP 1988);

Rings, Fields and Groups: Introduction to Abstract Algebra, Reg Allenby (Butterworth-Heinemann, 2nd edition 1991).

Exam (80%, duration: 2 hours) in the summer exam period.
Coursework (20%) in the MT.